On Mon, Jul 11, 2016 at 1:22 PM, Ketan Maheshwari < ketancmaheshw...@gmail.com> wrote:
> Matthew, > > I am probably not using the right language but I meant that each element > has three indices associated with it: x, y, z. > > Here is a snapshot: > > 1 10 55 5.7113635929515209e-03 > 1 10 56 4.2977490038287334e-03 > 1 10 57 2.8719519782193204e-03 > 1 10 58 1.4380140927001712e-03 > 1 10 59 9.9299930690365083e-17 > 1 11 0 0.0000000000000000e+00 > 1 11 1 1.5658614070601917e-03 > 1 11 2 3.1272842098367562e-03 > 1 11 3 4.6798423857521204e-03 > > Where the first three columns are the coordinates and the last one is > value. > This is not a matrix. A matrix is a linear operator on some space with a finite basis: https://en.wikipedia.org/wiki/Matrix_(mathematics) This is just a set of data points. Most people would call this a vector, since you have an index I (which consists of each independent triple) and a value V. > Could you clarify the meaning of "diagonalization is not a clear concept" > if it is applicable to this case. > There is no one definition of tensor diagonalization. Matt > Thank you, > -- > Ketan > > > On Mon, Jul 11, 2016 at 1:15 PM, Matthew Knepley <knep...@gmail.com> > wrote: > >> On Mon, Jul 11, 2016 at 12:05 PM, Ketan Maheshwari < >> ketancmaheshw...@gmail.com> wrote: >> >>> Hello PETSC-ers, >>> >>> I am a research faculty at Univ of Pittsburgh trying to use PETSC/SLEPC >>> to >>> obtain the diagonalization of a large matrix using Lanczos or Davidson >>> method. >>> >>> The matrix is a 3 dimensional dense matrix with a total of 216000 >>> elements. >>> >>> After looking into some of the examples in PETSC as well SLEPC >>> implementations >>> it seems like most of the implementations are with 2 dimensional >>> matrices. >>> >> >> You will have to explain what you mean by a "3D matrix". A matrix, by >> definition, has only >> rows and columns. You may mean a matrix generated from a 3D problem. That >> should pose >> no extra difficulty. You may mean a 3-index tensor, in which case >> diagonalization is not a clear >> concept. >> >> Thanks, >> >> Matt >> >> >>> So, I was wondering if it is possible to express a 3 dimensional matrix >>> object >>> compatible to PETSC so that the SLEPC API could be used to obtain >>> diagonalization. >>> >>> Any suggestions or pointers to documentation or examples would be of >>> great >>> help. >>> >>> Best, >>> -- >>> Ketan >>> >>> >> >> >> -- >> What most experimenters take for granted before they begin their >> experiments is infinitely more interesting than any results to which their >> experiments lead. >> -- Norbert Wiener >> > > > > -- > Ketan > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener